The drive wheel of an engine is 13 inches in diameter, and the pulley on the rotary pump is 5 inches in diameter. If the shafts of the drive wheel and the pulley are 2 feet apart, what length of belt is required to join them?

23.66 in

Explanation:

Drive wheel of engine is larger than pulley of rotary pump

Drive wheel diameter = 13 in

Since radius = diameter / 2

drive wheel radius = 6.5 in

Pulley diameter = 5in

Pulley radius = 2.5 in

Horizontal Distance between pulleys = 2ft

Note : 1 foot = 12 inches

Converting distance to inches ;

Horizontal Distance between pulleys = 2×12 = 24 inches

Difference in height of pulleys = radius 1st pulley - radius of second pulley ;

Height difference = 6.5 - 2.5 = 4 in

From the diagram attached ;

AB = sqrt(BC^2 - AC^2)

Length of belt (AB) = sqrt( 24^2 - 4^2)

Length of belt = sqrt(576 - 16)

Length of belt = sqrt(560)

Length of belt = 23.66 in

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